What is the vertex of #y=(x-3)^2-25#?

Question

Hazel Anglin · Accepted Answer

Find the vertex of y = (x - 3)^2 - 25

Ans: vertex (3, -25)

This is the vertex form of y. Therefor, #Vertex (3, -25)#

Eli Assouline · Answer

#x_("vertex") = 3# Look at the explanation. I will let you take my stop point on to find #y_("vertex")#

#color(blue)(Method 1)#

What you are given in the question is in the format of 'completing the square'.

#color(brown)("Consider what is inside the brackets")# The -3 is negative but the answer is +3. So all you have to do is use the number (in this case it is 3) and change its sign.

Then as in Method 2; substitute for #x# to find #y# . In effect; method 1 is the same process as in method 2 it is just that it looks different

For completing the square the -3 in the bracket is obtained by multiplying the -6 in #-6x# by #1/2#. So completing the square has already 'done that bit'

#color(blue)("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")# #color(blue)(Method 2)# Write as: #y=x^2 -6x+3-25#

#y=x^2-6x-22..................(1)#

Consider the -6 from #-6x#

Then:

#x_("vertex") = (-1/2)xx(-6)=+3........(2)#

Substitute (2) into (1) and resolve for y which is the value of #y_("vertex")#

So you have #y_("vertex")= (3)^2-(6xx3)-22#

I will let you work that one out!

Eli Assouline · Answer

undefined The vertex of the function y = (x - 3)^2 - 25 is (3, -25).